The classical Grothendieck construction establishes an isomorphism between the (pseudo)functor $F:C\to Cat$ and the left Cartesian fibration $E\to C$. We can then show that $E$ is the lax colimit of the functor $F$.
This presentation is dedicated to the generalization of this result for $(\infty,\omega)$-categories. After defining $(\infty,\omega)$-categories, we will state the lax univalence for $(\infty,\omega)$-categories. We'll then explain how this result allows us to express a strong link between Grothendieck construction for $(\infty,\omega)$-categories and the lax-colimits of $(\infty,\omega)$-categories, similar to the classical case.